I Assuming nonlocal realism: What message would signal convey?

I have a strange relation to Bell's inequalities, I understand (so I hope) all the maths but have lots of trouble with the implications of their violation. Currently: Say we assume QM to be realistic, it can't be local. There needs to be some sort of instantaneous signalling.

Realism means that all measurement outcomes are predetermined. So all measurement outcomes of the second EPR particles are predetermined. Why does it need a signal from the first particle if the measurement outcomes are predetermined, i.e. what message does this signal convey?

When two particles are entangled, they exhibit correlations of their measured properties, even when they are spacelike separated. The correlation is peculiar however: it does not depend on an underlying value attached to the particles, but the correlation depends on what is measured on either side.

So, in case of two polarized photons, if Alice measures a certain polarization, then Bob's measurement is correlated with that measurement, and vice-versa. Since Alice can change the axis over which she measures at the last moment, the value she measures has to 'travel' superluminously to Bob to be able to make his measurement correlate with Alice's.

To actually quantize the correlation, several measurements have to be made to approach that value.

In fact, there is not really superluminal communication. What is really happening is subject to interpretation.

Ah okay, then it's actually the measurement parameters (i.e. the choice of the measurement basis) that somehow must find it's way to the second photon?

And what would in this case the "elements of physical reality" be that predetermine the measurements? Would they be functions like
##A:[0°,180°)\rightarrow\{+1,-1\}##
##B:[0°,180°)\times [0°,180°)\rightarrow\{+1,-1\}##

where ##A## determines if the first photon gets transmitted (+1) or absorbed (-1) based on the angle of its polarizer, and ##B## determines if the second photons gets transmitted or absorbed based on the angle of its polarizer AND on the angle of the first polarizer?

Ah okay, then it's actually the measurement parameters (i.e. the choice of the measurement basis) that somehow must find it's way to the second photon?

And what would in this case the "elements of physical reality" be that predetermine the measurements? Would they be functions like
##A:[0°,180°)\rightarrow\{+1,-1\}##
##B:[0°,180°)\times [0°,180°)\rightarrow\{+1,-1\}##

where ##A## determines if the first photon gets transmitted (+1) or absorbed (-1) based on the angle of its polarizer, and ##B## determines if the second photons gets transmitted or absorbed based on the angle of its polarizer AND on the angle of the first polarizer?

Yes, that is a good description of what a non-local realistic theory would look like.

Realism means that all measurement outcomes are predetermined. So all measurement outcomes of the second EPR particles are predetermined. Why does it need a signal from the first particle if the measurement outcomes are predetermined, i.e. what message does this signal convey?

No. This is only an (unfortunately very popular) misrepresentation. There exist realistic interpretations of quantum theory, and in these interpretations there is no such predetermination. Instead, what is misleadingly name "measurement result" is only a particular result of an interaction with something called "measurement device". The outcome of this particular experiment, in this situation, is predetermined, but depends not only on the state of the particle itself, but also on the state of the "measurement device". And, once for all the other imaginable "measurements", there is no "measurement device" and no corresponding state, these other "measurement results" remain undefined.

I guess non-local hidden variables are a candidate for non-local realism.

This can be imagined as a hidden value that is not bound to a location, that is: when the value is measured X at location A, it is also measured X at location B. This satisfies both realism (the value X) and non-locality.

I disagree. What has been rejected with Bell's theorem is, in fact, not local realism in any meaningful sense of the word "local". Because it makes no sense to say that some theory which even has some maximal speed of causal influence C is non-local only because this C is greater than the speed of light c. I think a meaningful definition of "local" could not use a particular value for such a maximal speed. If it uses some maximal speed, than it can use only that there exists some limiting speed, but cannot specify a number for it.

Ok, one can say that this is only a name, a convention, nothing more, the charges of chromodynamics have been named using colors, that's also completely arbitrary and completely wrong because it has nothing to do with colors. But this naming convention is not harmful, because it is not misleading anybody. The "convention" to name local theories with maximum speed C > c "nonlocal" is, unfortunately, extremely misleading. It makes many people believe that such theories would be somehow in contradiction with very fundamental beliefs about our world.

I disagree. What has been rejected with Bell's theorem is, in fact, not local realism in any meaningful sense of the word "local". Because it makes no sense to say that some theory which even has some maximal speed of causal influence C is non-local only because this C is greater than the speed of light c. I think a meaningful definition of "local" could not use a particular value for such a maximal speed. If it uses some maximal speed, than it can use only that there exists some limiting speed, but cannot specify a number for it.

Ok, one can say that this is only a name, a convention, nothing more, the charges of chromodynamics have been named using colors, that's also completely arbitrary and completely wrong because it has nothing to do with colors. But this naming convention is not harmful, because it is not misleading anybody. The "convention" to name local theories with maximum speed C > c "nonlocal" is, unfortunately, extremely misleading. It makes many people believe that such theories would be somehow in contradiction with very fundamental beliefs about our world.

I may be out of my league on this one, but I want to stress that I don't impose any speed of information; I just want to express the correlation between two measurements in terms of the measurements, with the caveat that the thing that is measured at both sides is the same. Since the variable is hidden and non-local, there is no superluminal transmission of information.

The result on one side, A, depends on the choice what to measure, b, on the other side. Above things are macroscopic and visible, thus, hidden variables are not relevant for this.

(Another possible explanation is that the result B depends on the choice a. Above explanations violate Einstein causality. So, one cannot save Einstein causality. But that above are valid explanations shows that one cannot use this for sending information - that would be in contradiction to at least one of the two explanations.)

The result on one side, A, depends on the choice what to measure, b, on the other side.

That is why I deem the hidden variable non-local; the information that X comprises is itself non-local. So what is bridged in spacetime by X can only be the measurement result. It works both-ways. X comprises information at both ends (e.g. the wavefunction). So what we have is exactly what QM predicts, there is no contradiction. That is why non-local hidden variables are more an interpretation than something else.

Ok, thanks. Let's now assume the opposite: Local, but non-realistic. So the functions I mentioned don't exist, but the signal doesn't either.

How can I imagine this? If there's no signalling, how can be there any correlation?

Non-realistic can mean a number of things. A lack of causality, for example - backward in time influences. Contextuality. Splitting of worlds. No one can really picture the mechanism.

However, that is not really any different than with non-local realistic theories such as Bohmian Mechanics. Saying there are non-local influences does not really explain all that much, as there are plenty of remaining questions. For example: how do objects become entangled (which they can) if they never even existed at the same time? BM does not feature signalling (influences) through time.

Non-realistic can mean a number of things. A lack of causality, for example - backward in time influences. Contextuality. Splitting of worlds. No one can really picture the mechanism.

A nice list of completely absurd - at least from a classical common sense point of view - possibilities. Except contextuality - which is compatible with realism and causality and a property of dBB theory.

However, that is not really any different than with non-local realistic theories such as Bohmian Mechanics.

You think so? A realistic and causal interpretation, the most strange thing is that it is not Einstein-causal. A property it shares with such classical common-sense-compatible theories like Newtonian gravity.

Saying there are non-local influences does not really explain all that much, as there are plenty of remaining questions. For example: how do objects become entangled (which they can) if they never even existed at the same time?

Easy to answer: By metaphorical use of human language. Entanglement is something which in dBB theory exists at a given moment of time.

Entanglement is something which in dBB theory exists at a given moment of time.

Which does not explain, in any mechanical sense, why something would be entangled with something else that does not even exist yet. And why the space-time diagram of that entangled system shows both forward- and backward-in-time connections.

My point is that "non-local realistic" is no more objectively reasonable or descriptive than "local non-realistic". Either one is an accepted interpretation and has followers.

My point is that "non-local realistic" is no more objectively reasonable or descriptive than "local non-realistic". Either one is an accepted interpretation and has followers.

I do not care about numbers of followers and acceptance at all. I care about correspondence to reality. For me, the difference is fundamental. If the world does not really exist, what would be the point doing science? One can, as well, play nice games, say, Go, or some adventure games. The ability to compute some cross-sections for particle accelerators is not interesting in itself, it makes sense only as a tool to study reality.

Which does not explain, in any mechanical sense, why something would be entangled with something else that does not even exist yet. And why the space-time diagram of that entangled system shows both forward- and backward-in-time connections.

I thought that dBB solved this by positing an absolute reference frame.

For example: how do objects become entangled (which they can) if they never even existed at the same time?

First, in BM particles are not entangled. Pilot waves are.

Second, in entanglement swapping, even if the final wave functions never existed at the same time and space, their ancestor wave functions did. This is analogous to the fact that my genes are correlated with the genes of my cousin who I never met; we are correlated because we have the common ancestors.